# Math Help - World Problem dealing with matrices

1. ## World Problem dealing with matrices

Please help me to understand this problem, if I understand how to set it up I know I can solve it. . .

Problem: Candidate A and candidate B are running for mayor of a small town. After attending a debate, some citizens change their minds about the candidate for whom they will vote. Let m = 25% be the percent of citizens that switch from candidate A to candidate B. Let n = 16% be the percent of citizens that switch from candidate B to candidate A. Before the debate, candidate A was expected to win the election 1200 votes to 950 votes. After the debate, how many vots will candidate A and candidate B recieve? Use the transition matrix T to help you answer the question.

[1-m n] = T
[ m 1-n]

2. $
\left(\begin{array}{cc}1-.25&.16\\.25& 1-.16\end{array}\right)
$

then
$
\left(\begin{array}{cc}.75&.16\\.25& .84\end{array}\right)$
= T
so
$\left(\begin{array}{cc}.75&.16\\.25& .84\end{array}\right)$ $\left(\begin{array}{cc}1200\\950\end{array}\right)$
when multiplied out we get
$\left(\begin{array}{cc}952\\1245.8\end{array}\righ t)$